Homework Help:
Quantum Mechanics, one-dimensional box problem

What are the energy eigenfunctions and eigenvalues for the one-dimensional box problem describ above if the end of the box are at -a/2 and a/2

I can find the solution of this problem Phi(x) = Asin kx + Bcos kx
and property of wavefunction is continuous at boundary
Phi(x=-a/2) = Phi(x=a/2)=0
but i don't understand to find k (wave number), please help me

Can you sketch your eigenfunctions?
(I'm assuming you've done the box problem with ends x=0 to x=a. Hopefully you realize that the choice of origin shouldn't change the shape of the eigenfunctions.)
See any pattern? any grouping of the eigenfunctions?